Layer-selective proximity symmetry breaking enables anomalous and nonlinear Hall responses in $1H$-Nb$X_2$ ($X =$ S, Se, Te)
Nonlinear Hall responses provide an electrical probe of Berry-curvature dipoles, but they are symmetry forbidden in many pristine two-dimensional metals. We show that layer-selective magnetic proximity provides a symmetry-controlled route to induce and tune anomalous and nonlinear Hall responses in metallic monolayer $1H$-Nb$X_2$ ($X=\mathrm{S,Se,Te}$), where the nonmagnetic $D_{3h}$ crystal has vanishing anomalous Hall conductivity and Berry-curvature dipole. Fully relativistic density-functional theory combined with Wannier interpolation shows that an out-of-plane proximity exchange preserving $C_3$ generates a sizable sheet anomalous Hall conductivity, $σ^{\mathrm{sheet}}_{xy}\sim 10^{-2}(e^2/h)$ in representative active windows, while the Berry-curvature dipole remains zero. Breaking $C_3$ by introducing an in-plane exchange component, or by using an orthogonal two-sided exchange texture, produces a tunable Berry-curvature dipole and hence a nonlinear Hall response. Its exchange-odd part is linear in the in-plane exchange to leading order in the minimal model; the calculated spectra reach and can exceed $|D_y|\sim10^{-2}$$\mathring{A}$, with the largest and sharpest features in NbTe$_2$. These trends are rationalized by symmetry analysis and an interface-induced $k$-linear Rashba-Zeeman minimal model. Within the idealized proximity model, an orthogonal dual-interface geometry further provides component-selective sign reversal of first- and second-harmonic Hall signals in the same Hall-bar configuration.